An example of an asymptotically Hilbertian space which fails the approximation property Academic Article uri icon

abstract

  • Following Davic's example of a Danach space failing the approximation property (1973), we show how to construct a Danach space E which is asymptotically Hilbcrtian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is "almost" a weak Hubert space and which can be written as the direct sum of two subspaces all of whose subspaccs have the approximation property. 2001 P. G. Casazza, C. L. Garcia, and W. B. Johnson.

published proceedings

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Casazza, P. G., Garcia, C. L., & Johnson, W. B.

citation count

  • 8

publication date

  • April 2001